To find the unit rate of the washing machine filling with water, we need to determine how many gallons it fills per minute.
The washing machine fills at a rate of \(\frac{3}{4}\) of a gallon in \(\frac{1}{5}\) of a minute. To find the rate in gallons per minute, we should divide the amount of water (\(\frac{3}{4}\) of a gallon) by the time it takes (\(\frac{1}{5}\) of a minute).
So, the correct calculation for the unit rate is:
\[ \text{Unit rate} = \frac{3/4 \text{ gallons}}{1/5 \text{ minutes}} = \frac{3}{4} \div \frac{1}{5} \]
When dividing by a fraction, we multiply by its reciprocal:
\[ \frac{3}{4} \div \frac{1}{5} = \frac{3}{4} \times 5 = \frac{15}{4} \]
Thus, the unit rate is \(\frac{15}{4}\) gallons per minute, or \(3.75\) gallons per minute.
Don's mistake was in this calculation. Based on the options given:
- He originally calculated the unit rate incorrectly.
The correct choice from your options would be:
He divided \(\frac{3}{4}\) by \(\frac{1}{5}\) instead of multiplying \(\frac{3}{4}\) by \(\frac{1}{5}\).
This indicates that he misunderstood how to calculate the unit rate. He needed to divide, not multiply. Thus, the answer is:
He divided \(\frac{3}{4}\) by \(\frac{1}{5}\) instead of multiplying \(\frac{3}{4}\) by \(\frac{1}{5}\).